One of the first attempts to understand this issue was made in [1]}, in which
the Euclidean and Lorentzian terms given by Eqs.(REF ) and () are treated differently, by closely following the actual construction of LQG. To be more specific, in the full theory [2]}, the extrinsic curvature in the Lorentzian term () can be expressed in terms of the connection and the volume as
\(K^i_a=\frac{1}{\kappa \gamma ^3}\lbrace A^i_a,\lbrace \mathcal {H}_{\mathrm {grav}}^{(E)},V\rbrace \rbrace ,\) 
